The Swiss branch of British bank HSBC says the theft of data by a former employee affected about 15,000 Swiss client accounts.
Previously, HSBC said it affected no more than ten.
A former HSBC computer specialist admitted stealing client data from the bank which he passed to French tax authorities.
"It is now clear that the theft, which was perpetrated by a former IT employee about three years ago, involves approximately 15,000 existing clients who had accounts with the bank in Switzerland before October 2006," HSBC said.
Switzerland has always insisted it will not support use of the stolen data to answer requests from foreign authorities about tax issues.
Last month, the Swiss and French governments reached agreement over the fate of stolen bank client data.
As part of the deal to move forward with a double taxation agreement, France said it would not request administrative assistance in obtaining information about suspected tax evaders whose details were contained in the stolen data.
However, France retained the right to pass the information on to other countries.
Meanwhile, the Swiss financial regulator has announced that it has begun formal administrative proceedings against HSBC.
The Financial Market and Supervisory Authority (Finma) is investigating how the theft of the data could have happened. It also wants to know whether the "organisational and technical measures implemented by HSBC since this incident to prevent such occurrences comply with the legal requirements".
swissinfo.ch and agencies